Dynamical systems applied to dynamic variables of patients from the intensive care unit (ICU): Physical and mathematical mortality predictions on ICU

Abstract

Methodologies have been developed to evaluate the heart rate (HR) chaotic dynamics, differentiating normality of chronic and acute disease and the evolut ion between these states; other dynamic variables of system on ICU have shown a chaotic behavior. An induction from 8 patients was realized, five discharged alive from ICU and 3 cases of mortality, defining sets and subsets, as well as operations between them that differentiate and predict the dynamics of patients who survive of those with fatal outcome, through the maximum and minimum values of chaotic attractors of 4 dynamic variables: Heart rate (HR), arterial carbon dioxide partial pressure (PACO2), venous carbon dioxide partial pressure (PvCO2), and oxygen venous saturation (SVO2). Finally a blind study was done with 12 patients, calculating sensitivity, specificity, PPV, NPV and accu racy. Also a temporal decrease in the cardiac dynamics evaluation was done, from 21 to 15 hours, through an induction with two cases, one with normal dynamic and one with acute dynamic. The occupation spaces of cardiac chaotic attractors were measured, and then a blind study was realized with 18 patients, calculating sensitivity, specificity and Kappa coefficient. The equation T = [(B2 ∩ C2) U A1 U D3] U [(A2 ∩ B1) U C3 U D1] differentiates and predicts the dynamics of patients who survive of those with fatal outcome in the ICU. The sensitivity, specificity, PPV and NPV were 100%, and accuracy was 1. Acute cardiac dynamic was differentiated of normal dynamic on 15 hours, allowing to reduce the time of the evaluation of this dynamic of 21 to 15 hours, the sensitivity and specificity values were 100% and Kappa coefficient was 1. Dynamical systems in the context of set algebra allow differen tiate patients who are discharged alive from those with an adverse outcome. The evolution to death can be predicted in a physical and mathematical way in the ICU.